It should be point out that compared with [1]}, the limiting process in the case of BFD equation is more complex. The parameters \((\rho _B,\mathfrak {u}_B,T_B)\)  of local Maxwellian \(M=\frac{\rho _B}{(2\pi T_B)^{3/2}}\exp \lbrace -\frac{|v-\mathfrak {u}_B|^2}{2 T_B}\rbrace \)  can be determined by the compressible Euler equations deduced from classical Boltzmann equation
\(\left\lbrace \begin{aligned}&\partial _t \rho _B+\nabla _x\cdot (\rho _B \mathfrak {u}_B)=0,\\&\partial _t(\rho _B \mathfrak {u}_B)+\nabla _x\cdot (\rho _B \mathfrak {u}_B\otimes \mathfrak {u}_B)+\nabla _x p=0,\\&\partial _t \left(\frac{1}{2}\rho _B|\mathfrak {u}_B|^2+\frac{3}{2}\rho _B T_B\right)+\nabla _x\cdot \left[\,\rho _B \mathfrak {u}_B\left(\frac{1}{2} |\mathfrak {u}_B|^2 +\frac{3}{2}T_B\right)\,\right] + \nabla _x\cdot (p\mathfrak {u}_B)=0.\end{aligned}\right. \qquad \mathrm {(CEB)}\) 
